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Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed
Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
Semiconductor qubits for adiabatic quantum computing
Malcolm Carroll
Sandia National Labs, Albuquerque
June 11th, 2014
Spin read-out & Rabi oscillations Silicon P donor qubit structure
~10 P
P
Local ESR
Adiabatic inversion
Ramp time [us]
DQD qubits for QA
• Motivation for Si qubit research in adiabatic QC and QA
• Single electron spin qubit and adiabatic operation
• Semiconductor qubit approaches to quantum annealing
• Summary
Outline
2
What are the limits and extensions of adiabatic control of one or several qubits? (e.g., adiabatic inversion)
Questions about quantum annealing
• Are there tests with one and a few qubits that inform the “black box” testing approach
• What are the microscopic dynamics and how does it break?
o Is fast relaxation helpful? (what dependence?)
o kT >> Egap ?
o What role does T2 play?
• What makes a good qubit for quantum annealing?
o Is there benefit to using a semiconductor qubit for QA?
Our approach:
• Examine silicon (or semiconductor) qubits in context of adiabatic quantum computation (or annealing)
Motivations and research direction
?
4
• Motivation for Si qubit research in adiabatic QC and QA
• Single electron spin qubit and adiabatic operation
• Semiconductor qubit approaches to quantum annealing
• Summary
Outline
5
Kane-like (electron spin only):
Single donor for qubit
One electrode on/off – frequency tuning to NMR or ESR u-waves
Second electrode on/off – overlap electrons for exchange (sqrt[SWAP])
Lot’s of progress in this area recently
Not clear how people will couple donors but focus of this talk is context of adiabatic control for single spin
Qubit approach using donors in Si
Kane, Nature, 1998
6
Concept
SET or QD detects nearby charge center ionization
Spin dependent ionization
Single donor spin read-out concept
7 Morello et al., Nature 2010
Charge state is static
Charge state is changing in time due to tunneling
2. Read
1. Load
3. Unload
Read sequence (spin up)
SET donor EC
Poly silicon quantum dot
1.2V 0 V
0 V 0 V
Si
SiO2
current
Poly-Si
• Simplify SET for donor read-out o Implant will be self-aligned
Harvey-Collard
500 nm
LP RP
8
S/D
E=𝑞
𝐶
Single dot
Poly silicon quantum dot
1.2V 0 V
0 V 0 V
Si
SiO2
current
Poly-Si
• Simplify SET for donor read-out o Implant will be self-aligned
• Relatively regular period Coulomb blockade achieved in poly silicon SET
• Wire width ~50-60 nm with gaps between wire and plunger of ~40-50 nm
• This structure can regularly be used for read-out
Harvey-Collard
500 nm
LP RP
9
S/D
E=𝑞
𝐶
Single dot
QCAD is semi-classical simulation capability developed at SNL
1.1x1017/cm3 charge fits 4K threshold
Order of ~5x1010/cm2
Gate to quantum dot capacitances are similar to QCAD predictions in multiple devices
Semi-classical modelling of lithographic dot
Shirkhorshidian
Dot location
10
Typical implant conditions:
120 keV implant, range ~28 nm below SiO2/Si interface, 18 nm vertical straggle
4e11/cm-2 dose → ~ 14 Sb donors in 60 x 60 nm2 window
Charge offsets are seen in these implanted poly-MOS devices
Gate wire with implant – QD coupling to donor
Si
SiO2
Poly-Si
Sb
T ~ 2K
11
Implant window
Tuning spin readout
12
Spin bump with 256 averages
Measure Unload Load
Ez
Reservoir
Donor
Ez Reservoir
Ez Reservoir
Load
Read
Unload
Lilly
up
All down would have no “bump”
ESR pulse sequence – two level pulse
13
1. At the end of the readout pulse, a spin down is loaded. (b) 2. Pulse energy levels down to manipulate. (a) 3. Apply microwaves. (a) 4. Spin readout (b)
Donor
Ez
Reservoir Donor
Ez Reservoir
(a) plunge and ESR (b) read
Electron spin resonance of single spin
14
o Two level test with ESR detects spin resonance o Phosphorus implanted sample (~ 400 nm from center) o Similar approach to Al-Si SET devices [Pla et al. (2012)]
Nguyen
B=1.3T P = 0 dBm
Read/initialize level Hold/u-waves
Time [ms]
14
Resonance frequency drifts
15
These two scans were taken 10 min apart.
p
Electron spin
Nuclear spin bath
o 29Si can reorient over timescales of ~sec, and the electron resonance frequency shifts due to hyperfine coupling.
o ~5-10 MHz line width or equivalent of ~ 0.2-0.3 mT o Bac max ~0.1 mT
Lilly
Incomplete pulsed X rotations due to spin bath diffusion
16
• 128 averages per trace • 150 repeats • Fixed frequency (36.459 GHz)
• For a fixed rotation (~pi pulse)
time: • sometimes the spin signal
is small, sometimes large
Lilly
Microwave field dependence
17
z
x’
Bx
z
x’
Bx
0 dBm 3 dBm 6 dBm
frabi= 1.4 MHz frabi= 2.8 MHz frabi= 2.1 MHz
Lilly
Magnetization follows a complicated track
Constant precession around Z-axis can be separated out in rotating frame
ESR pulse for X rotation is notionally a diabatic pulse when on resonance
Adiabatic inversion starts off resonantly and transitions slowly through resonance (LUBO)
Rotating frame
Adiabatic inversion (pi rotation)
i
k
18
Adiabatic sweep compared to on-resonant pulse
Spin
bu
mp
sig
nal
Pulsed pi rotation “on resonance” Adiabatic Sweep Hold Read Read Hold
Luhman
Df/t<<frabi
2
Df=25 MHz; t=10 us
Adiabatic approach
19
p
Electron spin
Nuclear spin bath
Characterization of adiabaticity of sweep
-5 dBm 0 dBm
Luhman 20
• Motivation for Si qubit research in adiabatic QC and QA
• Single electron spin qubit and adiabatic operation
• Semiconductor qubit approaches to quantum annealing
• Summary
Outline
21
List of metrics for QUBO example Physics of encoding
• Z, ZZ, X interactions & low measurement error (also independent control) • Tqubit loss
Metric: Max. time of computation because no error correction for leakage in quantum annealing
• Large (Egap)2 / tcomputation-time Measure: computation time limit before excitation error due to Landau-Zener tunneling This will be a prefactor in the scaling as gap of problem shrinks exponentially Excited state manifold of single qubit should also be well separated
• Texcite/ (Egap)2 at Egap ~O(kT) Measure: probability of thermal excitation error relative to computation time limit Notionally, fast adiabatic passage relative to thermal excitation time (even if kT > gap) Also details of the specific qubit interaction with its open system could be important in scaling
How important is cascade of low weight Hamming error to larger Hamming error? What Hamming distance are the bath interactions for each qubit instance?
• Correlation length (?) Need a metric for coupling between high weight Hamming transitions Notionally, large domains “coherently tunneling” to find energetic minima (non-classical hopping)
Engineering of encoding • Parameter-tuning-range/noise • High yield (uniformity – variance in parameters) or accurate characterization • Scalability (integration, routing, power)
What makes a good quantum annealing qubit?
22
List of metrics for QUBO example Physics of encoding
• Z, ZZ, X interactions & low measurement error (also independent control)
23
What makes a good quantum annealing qubit?
Single spin encoding
1
0
BZ
BX
Tt )0(
)0()( 2121212211 tHSSSSSSJSBSBH inityyxxzzzzzz
1. Difficult to tune local B-field for each spin
2. Exchange is not a true ZZ term
Two spin Hamiltonian
)(2121 tHmlkH initzzzz
| R > | L >
En
ergy
| L > | R >
Charge qubit encoding for QUBO
24
Modulation of k and l can be accomplished with voltages on gates
Negative and positive epsilon might range from -meV to +meV [~12-13 K]
Can be several orders of magnitude greater than the temperature in the dot
V
VH
0
02,1
Voltage
)(2121 tHmlkH initzzzz
Initialization
Tunneling magnitude is independently tunable from possibly less than neV to 100 ueV (likely greater)
Only positive
0
02,1 t
tH
''
0 RL
| R > | L >
En
ergy
| L > | R >
2 t
25
)(2121 tHmlkH initzzzz
Coulomb interaction for qubit coupling 26
Interaction magnitude experimentally found to range from 25-85 ueV [~0.25-1K]
Strength of Z1Z2 interaction tunable (by construction or FET couplers) & might be made larger
A little tricky to build pure ZZ but can minimize cross terms
H-litho using donors is possible path that might address both achieving high fidelity & biger ZZ
Van Weperen, PRL, 2011
L. Trifunovic et al., arXiv 1110.1342
26 Bussmann
27
Other interactions for charge qubit
Available interactions
• Z interaction • X interaction
ZZ interaction −ZZ interaction XX interaction XZ interaction
Speculative interactions
XZ Donors: Superior alignment? Previously proposed by Hollenberg et al.
27 Landahl, Jacobson
)(2121 tHmlkH initzzzz
Two spin approach
Motivation: • Try to leverage benefits of spin as qubit encoding (low effective kT near E-min-gaps) • k,l range is defined by magnitude of J for each DQD • 2-qubit coupling is similar approach as charge qubit
Challenge: • Possible problem with meta-stability (bigger problem for AMO approaches?) • S/T- also possible • Weak initialization fields for both? This sets max E of parameters (speed/size of computation limit?)
02,1
Z
Z
dB
dBJH
poly
B
Inductor? Bz,1 Bz,2
Qubit sub-space
| ↓↓ >
| ↑↑ > | ↑↓ > + | ↓↑ >
| ↑↓ > - | ↓↑ > En
ergy
V
J
28
• Motivation for research in adiabatic QC and QA
• Single electron spin qubit and adiabatic operation
• Semiconductor qubit approaches to quantum annealing
• Summary
Outline
29
List of metrics for QUBO example Physics of encoding
• Z, ZZ, X interactions & low measurement error (also independent control) • Tqubit loss
Metric: Max. time of computation because no error correction for leakage in quantum annealing
• Large (Egap)2 / tcomputation-time Measures: computation time limit before excitation error due to Landau-Zener tunneling Excited state manifold of single qubit should also be well separated
• T1/ (Egap)2 at Egap ~O(kT) Measures: probability of thermal excitation error relative to computation time limit Notionally, fast adiabatic passage relative to thermal excitation time (even if kT > gap)
What makes a good quantum annealing qubit?
30
?
List of metrics for QUBO example Physics of encoding
• Z, ZZ, X interactions & low measurement error (also independent control) • Tqubit loss
Metric: Max. time of computation because no error correction for leakage in quantum annealing
• Large (Egap)2 / tcomputation-time Measures: computation time limit before excitation error due to Landau-Zener tunneling Excited state manifold of single qubit should also be well separated
• T1/ (Egap)2 at Egap ~O(kT) Measures: probability of thermal excitation error relative to computation time limit Notionally, fast adiabatic passage relative to thermal excitation time (even if kT > gap)
What makes a good quantum annealing qubit?
31
? Start with Si charge qubit as test platform
Charge qubit encoding for QUBO (example)
32
Charge qubit is based on two level approximation of DQD Encoding is left / right Gap is dependent on tunnel coupling between wells Detuning established with lateral electric field
e
|L> |R>
Nordberg et al., PRB 2009
Characterization of energy dependent relaxation
Developed measurement technique and analysis to extract relaxation time and dependence on energy
Related to work done by Harbusch et al. PRB 2010
Non-adiabatic (fast ramp)
Adiabatic (slow ramp)
34
?
Square pulse (f & r)
tmeasure
tramp
215 Hz 860 Hz
8600 Hz 3010 Hz
• Super-Ohmic model leads to peaks growing closer together with frequency • Ohmic spectral leads to different qualitative signature of peak merging • Super-ohmic fits experiment better – good fit with acoustic phonons
Illustrative model
Jacobson
35
arXiv:1403.3704
QIST contributors at SNL Qubit fab: M. Busse, J. Dominguez, T. Pluym, B. Silva, G. Ten Eyck, J. Wendt, S. Wolfley Qubit control & measurement: N. Bishop, S. Carr, M. Curry, S. Eley, T. England, M.
Lilly, T.-M. Lu, D. Luhman, K. Nguyen, M. Rudolph, P. Sharma, A. Shirkhorshidian, M. Singh, L. Tracy, M. Wanke
Advanced fabrication (two qubit): E. Bielejec, E. Bussmann, E. Garratt, A. MacDonald, E. Langlois, B. McWatters, S. Miller, S. Misra, D. Perry, D. Scrymgeour, D. Serkland, G. Subramanian, E. Yitamben
Device modeling: J. Gamble, T. Jacobson, R. Muller, E. Nielsen, I. Montano, W. Witzel, R. Young
Joint research efforts:
o Australian Centre for Quantum Computing and Communication Technology (D. Jamieson, A. Dzurak, A. Morello, M. Simmons, L. Hollenberg)
o Princeton University (S. Lyon) o NIST (N. Zimmerman) o U. Maryland (S. Das Sarma) o National Research Council (A. Sachrajda) o U. Sherbrooke (M. Pioro-Ladriere) o Purdue University (G. Klimeck & R. Rahman) o U. New Mexico (I. Deutsch, P. Zarkesh-Ha) o U. Wisconsin (M. Eriksson) o University College London (J. Morton, S. Simmons)
QIST team & external connections
36
Summary
37
o Silicon electron spin qubit is platform for ESR experiments (limits of adiabatic control?) • Fairly well understood noise
o Adiabatic control scheme improves spin inversion probability • This is the same control as LUBO • Background nuclear spins in natural silicon produce diffusion of resonant frequency
o Discussed different encodings of semiconductor qubits for quantum annealing • DQD could work (charge or spin) • Possible advantages in min-gap energy, fab precision (i.e., accurate Hamiltonian) &
perhaps relaxation dynamics • Two pulse scheme identified as general way to characterize spectral density of
relaxation processes • Si MOS charge qubit spontaneous emission consistent with acoustic phonons
Spin read-out & Rabi oscillations Silicon P donor qubit structure
~10 P
P
Local ESR
Adiabatic inversion
Ramp time [us]
DQD qubits for QA
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